#8 i meant to post #4 (8) Find the function whose Fourier transform is f(k)- (9) Find the solution to the heat equation on the real line have the initial (b) Use your Green's function to...
please I need solution as soon as possible Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = uti 0<x< 6; t>0; B.C.: uz (0.t) = 0; ux(6,t) = 0; t> 0; 1. C. :U(x,0) = 12 + 5cos (6x) – 4cos(2x); 0<x<6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (6) Determine whether the boundary...
1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) to find the value of the integral o0 cos kx dk 0 1 +k2 (c) Show explicitly that Parseval's theorem is satisfied for eand its Fourier transform 1. Consider the function f(x)-e- (a) Find its Fourier transform. (b) Use the result of part (a) to find the value of the integral o0 cos kx dk 0 1 +k2 (c) Show explicitly that Parseval's...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the temperature at ? = 3? (Use...
3. Consider the non homogeneous heat equation ut- urr+ 1 with non homogeneous boundary conditions u(0. t) 1, u(1t) (a) Find the equilibrium solution ueqx) to the non homogeneous equation. (b) The solution w(r, t) to the homogenized PDE wt-Wra, with w(0,t,t)0 1S -1 Verify that ugen(x, t)Ue(x) +w(x, t) solves the full PDE and BCs (c) Let u(x,0)- f(x) - 2 - ^2 be the initial condition. Find the particular solution by specifying all Fourier coefficients 3. Consider the...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
9. (a) Find the inverse Fourier transform of the following function 1 (2 iw)(5 iw) (b) The displacement of a particular mechanical system is governed by the following ordinary differential equation dy 10y f(t) 7 dt where y(t) is the displacement and f(t) is the applied load Page 2 of 4 MATH2124 SaMplE EXAM IV i Use the Fourier transform to obtain the impulse response h(t) of the mechanical system (ii) If the applied load is f(t) = H (t1)-...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C. : Ux(0,t) = 0; Ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(21x); 0 < X < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the temperature at ? = 3? (Use...
a) Use MATLAB to find the Fourier Transform F(w) of the following function f(t). b) Plot F(w). Express the x-axis in [Hz]. Plot for f = -8Hz to 8Hz. f(t) = cos(27 (34))e-**" 0.8 0.6 0.4 0.2 f(t) appears to oscillate at 3 cycles/sec 0 -0.2 -0.4 -0.6 0.8 -1 2 -1.5 -0.5 0 0.5 1 1.5 2